Get the Princess!

[GeoTrail]

This sounds really similar http://en.wikipedia.org/wiki/The_Lady,_or_the_Tiger%3F

I've made a simple graphic that might help figure out the solution

[Trond]

@Trond: Thanks for correcting my typo in the 'given' statement. The rest of the logic holds however. Do you see any logical errors in what I posted?

I will have a look at it. Actually, I have a typo as well, because it can be logically proven that there must be a tiger in room 2 and 8, not 3 and 8 as I wrote. Room 3 can never have a tiger.

[Trond]

If #3 is True then room #2 is empty

Nope. If 3 is true, then 2 cannot be empty.

3. Room 2 and 7 are not empty.

but we know that room #2's sign is both True and False ( and thus contains neither the princess (True) nor the tiger (False)

No, it contains a tiger and is false. The whole concept of "fluctuating thruthness" just doesn't work.

[Demivec]

but we know that room #2's sign is both True and False ( and thus contains neither the princess (True) nor the tiger (False)

No, it contains a tiger and is false. The whole concept of "fluctuating thruthness" just doesn't work.

@Trond: From my perspective that would be the heart of the matter. A better term would be infinite regress.

As I mentioned earlier, I observed that there were three sets of them, {2, 5, 6}, {3, 8}, and {1, 4}. In each case the truth of a sign directly affects the truthfullness of another sign. I'll walk through the simplest one involving #1 and #4, it only regresses under some of the possibilities.

I'll walk through the example.

#1 -- Room #4 is not empty.
#4 -- Room #1 is not empty.

Both signs state that another room contains something. If the room contains the princess the room's sign is true, if it contains a tiger the room's sign is false.

If #1 contains the princess then it's sign is true and room #4 must contain a tiger (the princess is in room #1).
--> If room #4 contains a tiger, it's sign is false. Room #1 is therefore empty.
--> If room #1 is empty it cannot contain the princess.
**dead end**
A dead end is also reached if #4 contains the princess.

If #1 contains the tiger then it's sign is false and room # 4 must be empty.
**this conclusion is possible**
If #4 contains the tiger then it's sign is false and room #1 must be empty.
**this conclusion is possible**
Either one of the above conclusions is true or both rooms are empty and have false signs. All that matters is that the princess be in neither #1 nor #4.


The other signs involve conjunctive conditions and I provided some long winded examples already of those.



I regret I don't have anything additional to add. I have simply (or not so simply) come to a different conclusion. Thanks for the puzzle challenge, it was fun.


@GeoTrail: Nice illustration.

[GeoTrail]

@GeoTrail: Nice illustration.

Thanks

[utopiomania]

"The sign on the door of the princess was true"

"7. The princess is in a room with an odd number."

The sign on door 7 is unchallenged, isn't it? So she is in room 7. The rest is just smoke and mirrors.

[Thorium]

"The sign on the door of the princess was true"

"7. The princess is in a room with an odd number."

The sign on door 7 is unchallenged, isn't it? So she is in room 7. The rest is just smoke and mirrors.

No. You dont know if it's true and if it's true it could be any other room with a odd number.

[utopiomania]

No. You dont know if it's true

Why not?

Which of the other signs says that 7 is not true?

And if it IS true, "The sign on the door of the princess was true" says that she is behind sign 7.

[nco2k]

maybe the "princess" is a female tiger of noble blood?

edit: no wait.. the tiger ate the princess.



c ya,
nco2k

[Trond]

A better term would be infinite regress.

Ok, I understand now. I think your basic logic is solid, but you overinterpret it when making it into sign truth values.

8. This room contains a tiger and sign 3 is false. == If (#8 contains tiger) and (#3 is false) then #8 is true, else #8 is false.
3. Room 2 and 7 are not empty. == If (#2 <> empty) and (#7 <> empty) then #3 is true, else #3 is false.

If #8 is true the room contains a tiger -> if #8 contains a tiger it has to be False -> if #8 is False it cannot contain a tiger or sign #3 is True ( via !(A and B) = (!A or !B) ).

The key here is realizing that 8 only is fluctuating if it contains a tiger and sign 3 is false. If sign 3 is true, then the truth value of 8 stop fluctuating. Thus we know that sign 3 must be true.

but we know that room #2's sign is both True and False

No sign can be both true and false. Either it's true, or it's false. It can be logically proven that sign 2 is always false. Thus it cannot contain the princess, but it may contain a tiger. Here too is the key in realizing that the truth value of 2 is fluctuating if you set the sign to true, but it is not fluctuating (it stays false) if you set the sign to false. Thus we know it must be false.

[Thorium]

Which of the other signs says that 7 is not true?

No, but no sign says that it is true. So you dont know it. You have to look at the other rooms.

[PMV]

No one read my post? ... was that english so bad?
I could write it in german and another can translate it

MFG PMV

[Trond]

No one read my post? ... was that english so bad?
I could write it in german and another can translate it

MFG PMV

If princess in room 1 or 4, then one is true and not empty, so the other room must contain the tiger and the sign must be false, but then the sign is true. No princess.

Correct.

If princess in room 2, the sign must be true, but then it can't be true, because then princess is not allowed to be in this room. No princess.

Correct.

If princess in room 3, sign 2 and 7 are true.

Nope. If princess is in room 3, sign 2 and 7 must be false. Because sign 3 says room 2 and 7 are not empty. So there must be something in them. In other words, if princess is in room 3, there must be tigers in room 2 and 7. And that means these have to be false, not true.

If princess in room 5, sign 6 must be true. Sign 6 needs sign 2 to be false. Sign 2 needs sign 5 to be false, but there should be the princess, impossible. No princess.
If princess in room 6, the problem will be repeated. No princess.

Correct.

If princess in room 7, the 7 must be a odd number, true. Princess can be here.

Correct.

If princess in room 8, the sign says there is a tiger, so it can't be. No princess

Correct.

[GeoTrail]

The Princess didn't want to wait anymore, so she has gone to a spa. She's going to be back soon, to room 7.

[PMV]

If princess in room 3, sign 2 and 7 are true.

Nope. If princess is in room 3, sign 2 and 7 must be false. Because sign 3 says room 2 and 7 are not empty. So there must be something in them. In other words, if princess is in room 3, there must be tigers in room 2 and 7. And that means these have to be false, not true.

lol, i should read carefully, i had read "room 2 or 7" but it is "room 2 and 7"

correction:
if princess in room 3, sign 7 must be false because there must be a tiger. 3 is an odd number, so sign 7 would be true. No princess.


the result is the same


MFG PMV